{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模拟梯度下降法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-1.  , -0.95, -0.9 , -0.85, -0.8 , -0.75, -0.7 , -0.65, -0.6 ,\n       -0.55, -0.5 , -0.45, -0.4 , -0.35, -0.3 , -0.25, -0.2 , -0.15,\n       -0.1 , -0.05,  0.  ,  0.05,  0.1 ,  0.15,  0.2 ,  0.25,  0.3 ,\n        0.35,  0.4 ,  0.45,  0.5 ,  0.55,  0.6 ,  0.65,  0.7 ,  0.75,\n        0.8 ,  0.85,  0.9 ,  0.95,  1.  ,  1.05,  1.1 ,  1.15,  1.2 ,\n        1.25,  1.3 ,  1.35,  1.4 ,  1.45,  1.5 ,  1.55,  1.6 ,  1.65,\n        1.7 ,  1.75,  1.8 ,  1.85,  1.9 ,  1.95,  2.  ,  2.05,  2.1 ,\n        2.15,  2.2 ,  2.25,  2.3 ,  2.35,  2.4 ,  2.45,  2.5 ,  2.55,\n        2.6 ,  2.65,  2.7 ,  2.75,  2.8 ,  2.85,  2.9 ,  2.95,  3.  ,\n        3.05,  3.1 ,  3.15,  3.2 ,  3.25,  3.3 ,  3.35,  3.4 ,  3.45,\n        3.5 ,  3.55,  3.6 ,  3.65,  3.7 ,  3.75,  3.8 ,  3.85,  3.9 ,\n        3.95,  4.  ,  4.05,  4.1 ,  4.15,  4.2 ,  4.25,  4.3 ,  4.35,\n        4.4 ,  4.45,  4.5 ,  4.55,  4.6 ,  4.65,  4.7 ,  4.75,  4.8 ,\n        4.85,  4.9 ,  4.95,  5.  ,  5.05,  5.1 ,  5.15,  5.2 ,  5.25,\n        5.3 ,  5.35,  5.4 ,  5.45,  5.5 ,  5.55,  5.6 ,  5.65,  5.7 ,\n        5.75,  5.8 ,  5.85,  5.9 ,  5.95,  6.  ])"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "source": [
    "plot_x = np.linspace(-1., 6., 141)\n",
    "plot_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 2.5就是plot_x数组的平均值\n",
    "plot_y = (plot_x-2.5)**2 - 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(plot_x, plot_y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 浮点数存在误差，所以精度不能设置为0\n",
    "epsilon = 1e-8\n",
    "# 学习率\n",
    "eta = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "2.499891109642585\n-0.99999998814289\n"
    }
   ],
   "source": [
    "# 损失函数\n",
    "def J(theta):\n",
    "    return (theta-2.5)**2 - 1.\n",
    "\n",
    "# 导数函数\n",
    "def dJ(theta):\n",
    "    return 2*(theta-2.5)\n",
    "\n",
    "# 初始点\n",
    "theta = 0.0\n",
    "\n",
    "# 梯度下降的循环\n",
    "while True:\n",
    "    gradient = dJ(theta)\n",
    "    last_theta = theta\n",
    "    theta = theta - eta * gradient\n",
    "    \n",
    "    if(abs(J(theta) - J(last_theta)) < epsilon):\n",
    "        break\n",
    "    \n",
    "print(theta)\n",
    "print(J(theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "theta = 0.0\n",
    "theta_history = [theta]\n",
    "while True:\n",
    "    gradient = dJ(theta)\n",
    "    last_theta = theta\n",
    "    theta = theta - eta * gradient\n",
    "    theta_history.append(theta)\n",
    "    \n",
    "    if(abs(J(theta) - J(last_theta)) < epsilon):\n",
    "        break\n",
    "\n",
    "plt.plot(plot_x, J(plot_x))\n",
    "plt.plot(np.array(theta_history), J(np.array(theta_history)), color=\"r\", marker='+')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "46"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "# 45次查找和一次初始值\n",
    "len(theta_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "theta_history = []\n",
    "\n",
    "def gradient_descent(initial_theta, eta, epsilon=1e-8):\n",
    "    theta = initial_theta\n",
    "    theta_history.append(initial_theta)\n",
    "\n",
    "    while True:\n",
    "        gradient = dJ(theta)\n",
    "        last_theta = theta\n",
    "        theta = theta - eta * gradient\n",
    "        theta_history.append(theta)\n",
    "    \n",
    "        if(abs(J(theta) - J(last_theta)) < epsilon):\n",
    "            break\n",
    "            \n",
    "def plot_theta_history():\n",
    "    plt.plot(plot_x, J(plot_x))\n",
    "    plt.plot(np.array(theta_history), J(np.array(theta_history)), color=\"r\", marker='+')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "eta = 0.01\n",
    "theta_history = []\n",
    "gradient_descent(0, eta)\n",
    "plot_theta_history()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "424"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "len(theta_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "eta = 0.001\n",
    "theta_history = []\n",
    "gradient_descent(0, eta)\n",
    "plot_theta_history()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "3682"
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "len(theta_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "eta = 0.8\n",
    "theta_history = []\n",
    "gradient_descent(0, eta)\n",
    "plot_theta_history()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "OverflowError",
     "evalue": "(34, 'Result too large')",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mOverflowError\u001b[0m                             Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-15-89c87a003181>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0meta\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m1.1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mtheta_history\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mgradient_descent\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0meta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m<ipython-input-9-46124331ca03>\u001b[0m in \u001b[0;36mgradient_descent\u001b[1;34m(initial_theta, eta, epsilon)\u001b[0m\n\u001b[0;32m     11\u001b[0m         \u001b[0mtheta_history\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     12\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 13\u001b[1;33m         \u001b[1;32mif\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mJ\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mJ\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlast_theta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m<\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     14\u001b[0m             \u001b[1;32mbreak\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     15\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-6-0e251a46e054>\u001b[0m in \u001b[0;36mJ\u001b[1;34m(theta)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# 损失函数\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mJ\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m2.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;31m# 导数函数\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mOverflowError\u001b[0m: (34, 'Result too large')"
     ]
    }
   ],
   "source": [
    "# eta太大导致损失函数的值越来越大\n",
    "eta = 1.1\n",
    "theta_history = []\n",
    "gradient_descent(0, eta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 程序运行时像上面抛出异常不好。进行异常处理\n",
    "def J(theta):\n",
    "    try:\n",
    "        return (theta-2.5)**2 - 1.\n",
    "    except:\n",
    "        return float('inf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 进行异常处理之后可能会陷入死循环，所以加入重复次数最大值，以防止重复次数过大\n",
    "def gradient_descent(initial_theta, eta, n_iters = 1e4, epsilon=1e-8):\n",
    "    \n",
    "    theta = initial_theta\n",
    "    i_iter = 0\n",
    "    theta_history.append(initial_theta)\n",
    "\n",
    "    while i_iter < n_iters:\n",
    "        gradient = dJ(theta)\n",
    "        last_theta = theta\n",
    "        theta = theta - eta * gradient\n",
    "        theta_history.append(theta)\n",
    "    \n",
    "        if(abs(J(theta) - J(last_theta)) < epsilon):\n",
    "            break\n",
    "            \n",
    "        i_iter += 1\n",
    "        \n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eta = 1.1\n",
    "theta_history = []\n",
    "gradient_descent(0, eta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "10001"
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "source": [
    "len(theta_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "eta = 1.1\n",
    "theta_history = []\n",
    "gradient_descent(0, eta, n_iters=10)\n",
    "plot_theta_history()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.6.8 64-bit ('anaconda': conda)",
   "language": "python",
   "name": "python36864bitanacondaconda085db2e8b14649f4b32196068f7124e9"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}